Basic Trope: A character takes a seemingly fatal amount of damage, yet survives.
Straight: Alice beats Emperor Evulz, then throws him off a cliff and drowns him. He shows up a few episodes later, ready for revenge.
Exaggerated: Alice beats Emperor Evulz, then throws him off a cliff, drowns him, and orders a tactical airstrike over that part of the sea. She then orders a giant fishing boat to fish those waters clean and freeze everything they catch. However, despite all this, Emperor Evulz still comes back.
Emperor Evulz is very resilient. It takes a truly amazing amount of punishment to do him in.
That's not really Emperor Evulz she killed. He just made a weak doppelganger to fool Alice.
Emperor Evulz had a way of healing quickly, possibly Healing Factor or a device, and can only be killed if that's neutralized first.
Inverted: Emperor Evulz dies permanently as soon as Alice displays the slightest bit of force.
Alice is uneasy, expecting him to return at any moment. After a while, it becomes clear that he's dead for real.
The Emperor Evulz who reappears turns out to be an impostor.
However, after a few months, he comes back, explaining that he only survived because he put himself into a temporary death state to survive her onslaught of attacks.
...An impostor hired by the real Emperor Evulz, who's still in intensive care from his not quite fatal wounds.
Parodied: Emperor Evulz has an overly long "death" animation.
Zig Zagged: Alice is expecting Emperor Evulz to return at any moment. And after a while, he does. However, as soon as he appears and explains to Alice how he's still alive, she kicks his ass and kills him off for real.
Averted: Emperor Evulz dies the first time.
Enforced: "OK, so Emperor Evulz has a lot of fans who would get pissed if he died. But Alice is The Hero and she has to win. Wait, I've got it..".
Lampshaded: "I know you thought I was dead, but that's why pencils have erasers!"
Invoked: Emperor Evulz decides to goad Alice into throwing him into the ocean so he can live to fight another day.
Exploited: Emperor Evulz can't afford Alice disrupting the operations in his stronghold, so he faces her at a different location and "dies" so she'll believe her quest is done. While he recovers, business continues as usual.
Defied: Alice, not entirely sure that Evulz is dead, decides to go make sure.
Discussed: "I don't know...I know I just killed Evulz, but I have this incredibly odd feeling in the back of my mind that he's just going to show up again to fight me".
Conversed: "Ah, I know how this thing ends. Right after they begin their celebration party for finally having killed the bad guy, he's gonna show up, ready and raring for Round Two".
Evulz' survival truly stymies Alice, which in turn makes her feel like her only option is to give up fighting - if she can't truly kill him, what good is she?
Evulz' near-death experience deeply scars him, both physically and mentally. He develops an immense fear of Alice and falls into a deep depression.
Alice, though frightened at her archenemy's return, realizes that she has to train and get stronger in order to kill him for real.
Evulz trains himself to regain his lost strength and becomes even stronger than before, with the goal of crushing Alice and defeating his fear.